• Bernoulli
  • Volume 11, Number 6 (2005), 1059-1092.

On the convergence of the spectral empirical process of Wigner matrices

Z.D. Bai and J. Yao

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It is well known that the spectral distribution Fn of a Wigner matrix converges to Wigner's semicircle law. We consider the empirical process indexed by a set of functions analytic on an open domain of the complex plane including the support of the semicircle law. Under fourth-moment conditions, we prove that this empirical process converges to a Gaussian process. Explicit formulae for the mean function and the covariance function of the limit process are provided.

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Bernoulli, Volume 11, Number 6 (2005), 1059-1092.

First available in Project Euclid: 16 January 2006

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central limit theorem linear spectral statistics random matrix spectral distribution Wigner matrices


Bai, Z.D.; Yao, J. On the convergence of the spectral empirical process of Wigner matrices. Bernoulli 11 (2005), no. 6, 1059--1092. doi:10.3150/bj/1137421640.

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